Differential Equations Practice Questions

Class 12 · Mathematics · 2519 free MCQs with instant results and detailed explanations.

2519

Total

808

Easy

1216

Medium

495

Hard

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Topics in Differential Equations

Separation of Variables 594

General and Particular Solutions 569

Order and Degree 735

Homogeneous Equations 621

Sample Questions from Differential Equations

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Easy

What is the order of the differential equation dy/dx + y^2 = 0?

A. 1

B. 2

C. 0

D. Undefined

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Correct Answer: A

The order of a differential equation is determined by the highest derivative present. Here, the equation is first order since it has only the first derivative dy/dx.

Easy

In the differential equation d^2y/dx^2 + 3dy/dx + 2y = 0, what is the degree?

A. 1

B. 2

C. 3

D. 0

Show Answer & Explanation

Correct Answer: A

The degree of a differential equation is the power of the highest order derivative when the equation is a polynomial in derivatives. Here, it's first degree as the highest derivative d^2y/dx^2 is to the power of 1.

Easy

Which of the following differential equations is of the second order?

A. d^2y/dx^2 + y = 0

B. dy/dx + 2y = 1

C. d^3y/dx^3 - 5 = 0

D. dy/dx = e^x

Show Answer & Explanation

Correct Answer: A

A differential equation is of second order if it involves the second derivative. The first option includes d^2y/dx^2, making it second order, while others involve only first or third derivatives.

Medium

What is the order of the differential equation dy/dx + y^2 = 0?

A. 1

B. 2

C. 3

D. 0

Show Answer & Explanation

Correct Answer: A

The order of a differential equation is determined by the highest derivative present. Here, only the first derivative dy/dx is present.

Medium

Determine the degree of the differential equation x^2(d^2y/dx^2) + (dy/dx)^3 = x.

A. 1

B. 2

C. 3

D. undefined

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Correct Answer: C

The degree is the power of the highest order derivative after the equation is made polynomial in derivatives. Here, (dy/dx)^3 has the highest degree.

Medium

Which of the following equations is of the first order and first degree?

A. y'' + 3y' + 2y = 0

B. 2(dy/dx)^2 + y = 0

C. dy/dx + y = 5

D. d^2y/dx^2 + e^y = 0

Show Answer & Explanation

Correct Answer: C

An equation is of first order if it contains only the first derivative and first degree if it has derivatives raised only to the first power.

Medium

Find the order and degree of the equation (dy/dx)^2 + y = x.

A. Order 1, Degree 2

B. Order 2, Degree 1

C. Order 2, Degree 2

D. Order 1, Degree 1

Show Answer & Explanation

Correct Answer: A

The highest derivative is dy/dx which is first order, and the equation is quadratic in (dy/dx), giving it a degree of 2.

Hard

What is the order of the differential equation dy/dx + 3y = sin(x)?

A. 0

B. 1

C. 2

D. 3

Show Answer & Explanation

Correct Answer: B

The order is defined as the highest derivative present. Here, the highest derivative is dy/dx, which is of order 1.

Hard

Determine the degree of the equation y(dy/dx) = x.

A. 0

B. 1

C. 2

D. Not defined

Show Answer & Explanation

Correct Answer: B

The degree is the power of the highest derivative when the equation is polynomial in derivatives. Here, dy/dx is to the power of 1.

Q10

Hard

Which of the following equations is of order 2?

A. d²y/dx² + y = 0

B. dy/dx = y

C. d³y/dx³ + 2dy/dx = 0

D. y = e^x

Show Answer & Explanation

Correct Answer: A

Order is determined by the highest derivative; d²y/dx² indicates the highest order is 2.

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Differential Equations — Class 12 Mathematics Practice Questions Online

This page contains 2519 practice MCQs for the chapter Differential Equations in Class 12 Mathematics. The questions are organized by difficulty — 808 easy, 1216 medium, 495 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.